Find the Exact Value tan(90)

Problem

tan(90)

Solution

1. Identify the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

2. Substitute the angle 90 into the trigonometric functions.

tan(90)=sin(90)/cos(90)

3. Evaluate the sine and cosine of 90 using the unit circle.

sin(90)=1

cos(90)=0

4. Determine the value by substituting these results back into the fraction.

tan(90)=1/0

5. Conclude that since division by zero is not defined, the value does not exist.

Final Answer

tan(90)=undefined

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